Bribe, verb:
1. (Legal) A benefit (as money) given, promised, or offered in order to influence the judgment or conduct of a person in a position of trust (as an official or witness)
2. To influence or try to influence dishonestly by giving or promising something

Bribe, noun:
1. (Legal) A benefit (as money) given, promised, or offered in order to influence the judgment or conduct of a person in a position of trust (as an official or witness)
2. Something given or promised to a person in order to influence dishonestly a decision or action.

Extort, verb:
1. (Legal) To obtain (as money) from a person by force, intimidation, or undue or unlawful use of authority or power
2. To gain especially by ingenuity or compelling argument

Blackmail, noun: 1. (Legal) Extortion or coercion by often written threats especially of public exposure, physical harm, or criminal prosecution
2. The payment that is extorted

As you can see, they are all related, and all seem to involve some sort of deception or threat in order for a criminal to get what s/he wants from another person. The differences seem to lie in who the crime is against and what is at stake for the victim.

If you understand the differences, please post examples so we can help each other distinguish between them.

No. Your definitions are too narrow. They are correct, but incomplete. I present an example to counter yours, that follows the original post's definitions:

You have a girlfriend, and 500 parking tickets. She becomes your ex-girlfriend and threatens to tell the cops unless you pay her off. This is blackmail. You pay her, and she tells a cop anyway. The cop comes to your house and threatens you with a large fine unless you pay him off. This is extortion.

In this case, neither threat is physical or emotional-- they are both for a small amount of money to avoid paying a large amount. The difference is made clear in the differences in the authority of the individuals involved.

I would say that extortion has to do with the threat of some action you personally can take that will harm them, be it violence or the exercise of authority, but with the important caveat that it be an illegal action. Blackmail is threatening to reveal some information about someone, which is in most cases not against the law, it is only demanding compensation for NOT revealing it that is against the law. The example of the officer seems more like soliciting a bribe than extorting, since in this case the officer would not only be within their legal rights, but indeed be legally obliged to give you those tickets, but is giving you the option to instead pay them directly to ignore their legal obligation, and instead help cover up your "crimes". Of course, many times officials will demand "bribes" in order to do what they are technically supposed to be doing anyways, but which they have the authority to make much more difficult/impossible (such as, I am supposed to process your papers, but unless you pay me $20, I will do so at such a slow pace that they will, in effect, never be processed) which is really extortion, but phrased as a bribe (pay me $20 and I will "expedite" your paper processing, breaking my legal obligation to treat all applicants equally wink wink nudge nudge). When I think extortion though, I think of someone threatening to abuse their power if they aren't paid, whether that power be legal, or physical, or otherwise, and bribery is someone AGREEING to abuse their power in exchange for payment.

Extortion is not necessarily used to 'make someone do something' because they have 'their money'.

Extortion, for example, is someone has 'obtained' (either legally or illegally obtained) for example a 'document', which may reveal a very weak and vulnerable point and infrastructure of for example, a security company. Then that 'someone' decides to use this document against this security company, for many reasons, not only revolving around 'favours'.

What if someone told his landlord hey I saw you the other day at a motel six with a pretty young women, I was in that neighborhood testing out my new camera. I want to buy some expensive running cosmetics, but I only have enough for the rent what should I do, oh...do you think your wife would be interested in buying some cute pictures I took?